04/19/2304/19/23 5.3: Circumference and Area of Circles5.3: Circumference and Area of Circles

5.3: Circumferences and Areas 5.3: Circumferences and Areas of Circlesof Circles

Expectation:G1.6.1: Solve multistep problems

involving circumference and area of circles.

ACT Prep

In the standard (x,y) coordinate plane, the points (0,2), (8,2), (3,6) and (11,6) are the vertices of a quadrilateral. What is the area, in square units, of the quadrilateral?

A. 62B. 16C. 32D. 56E. 88

04/19/2304/19/23 5.3: Circumference and Area of Circles5.3: Circumference and Area of Circles

CirclesCircles

Defn: A circle is the set of all points in a plane that are the same distance, r, from a given point in the plane. The given point is known as the center of the circle, the distance is the radius of the circle and 2r is the diameter of the circle.

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CircumferenceCircumference

The circumference of a circle is the distance around the circle.

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pipi

Defn: pi (π): If a circle has circumference C units and diameter d units, then

π =

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CircumferenceCircumference

The circumference, C, of a circle with radius, r, and diameter, d, is:C =

04/19/2304/19/23 5.3: Circumference and Area of Circles5.3: Circumference and Area of Circles

Give the circumference of the circle below exactly and as an estimate to the nearest hundredth (do not forget units).

8 in

To give an exact answer, leave π in the answer.

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Area of a CircleArea of a Circle

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04/19/2304/19/23 5.3: Circumference and Area of Circles5.3: Circumference and Area of Circles

04/19/2304/19/23 5.3: Circumference and Area of Circles5.3: Circumference and Area of Circles

04/19/2304/19/23 5.3: Circumference and Area of Circles5.3: Circumference and Area of Circles

Area of a CircleArea of a Circle

The area, A, of a circle with radius, r, is given by the formula :

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A circle has radius 5 cm. Give the exact area in terms of π and the approximate area rounded to the nearest tenth.

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Give the exact area of the shaded part of the figure below.

38

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Determine the area of the shaded part of the figure.

r

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Sector of a CircleSector of a Circle

A sector of a circle is a part of a circle determined by an angle whose vertex is the center of the circle and whose sides intersect the circle (this is called a central angle).

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A Sector of a CircleA Sector of a Circle

O

A sector of circle O.

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Area of a Sector FormulaArea of a Sector Formula

If a sector of a circle has area of A square units, a central angle of N° and a radius of r units, then:A =

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The central angle of a sector of a circle has measure of 68°. If the circumference of the circle is 75.36 inches, what is the area of the sector?

What is the ratio of the area of the square to the area of the circle if the length of a side of the square is 10 units?

A.

B.

C.

D.

E.

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1

3

2

4

5

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Arc Length FormulaArc Length Formula

If an arc is determined by a central angle with measure of N°, then the length of the arc is calculated by the formula:

AL =

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Give another form for the Arc Give another form for the Arc Length Formula using the radius of Length Formula using the radius of

a circle.a circle.

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A circle has radius of 7 inches. What is the length of an arc determined by a sector whose angle measure is 30°?

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A circle has diameter of 28 cm. If a central angle has measure 36°, what is the arc length of the arc determined by the central angle? Calculate the probability that a randomly selected point of the circle lies in the sector.

Meg pounded a stake into the ground. When she attached a leash to both the stake and her dog’s collar, the dog could reach 9 feet from the stake in any direction. Using 3.14 for π, what is the approximate area of the lawn, in square feet, the dog could reach from the stake?

A.28B.57C.113D.254E. 283

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04/19/2304/19/23 5.3: Circumference and Area of Circles5.3: Circumference and Area of Circles

AssignmentAssignment

pages 317-319, # 8, 14-28 (evens), 29-38 (all)